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Weekly Updates8. STATISTICAL METHODS
All possible two dimensional error correction models were used to analyse the nonstationarity of the observed time series with Johansen cointegration rank tests. The hypotheses (H0: Rank=r, H1: Rank > r, r=0,1) of cointegrated data were rejected in all the models.
Two one dimensional time series are nonstationary, but their linear combination which is stationary does exist. Two such time series are cointegrated.
Time series {[x.sub.t], t = 0, 1, 2, ...} Granger causes time series {[y.sub.t], t = 0, 1, 2, ...} if in the model
[y.sub.t] = [[alpha].sub.0] + [m.summation over (i-1)] [[alpha].sub.i] [y.sub.t-i] + [m.summation over (i=1)] [[beta].sub.i] [x.sub.t-i] (1)
the F-test rejects the hypothesis that all coefficients [beta]'s are equal to zero.
Dickey-Fuller tests were performed and find that all one dimensional time series were nonstationary. But the first or the second differences where appropriate already were stationary and Granger causality Wald tests were applied to all these time series. And causality relations were obtained only in one pair of the variables. This analysis was appropriate because of the absence of the cointegration of all two dimensional time series (Engle and Granger, 1987; Brocklebank and Dickey, 2003; Tsay, 2005).
Statistical analysis was performed with SAS 9.1 ETS procedures.
9. CONCLUDING REMARKS BASED ON THE STATISTICAL ANALYSES AND GENERAL CONCLUSIONS
The absence of income and housing cost cointegration has also been presented by other authors (Gallin, 2006). In addition, our negative results on the possible causality of housing costs or affordability and loan interest rates or GDP may indicate a housing costs bubble.
The model for factors influencing housing costs incorporates general factors typical of economies in every country, as well as specific factors, typical of Lithuania, which has its own specific historical background, cultural heritage and mentality. The order of importance of these factors is taken at a more hypothetical value.
General factors: 1) gross domestic product per capita--as GDP grows, theoretically, so does the potential for increase in housing costs, 2) average net monthly income per working person--as this figure grows, theoretically, so does the potential for increase in housing costs; 3) average loan interest rates--as they grow, theoretically, so does the potential for a decrease in housing costs; 4) the divide between supply and demand--as this decreases, theoretically, the potential for a drop in housing costs increases. Specific factors: 1) features of the national Lithuanian character, which is known for having a low risk barrier, limited investment experience (focused mainly on reliable albeit low return investments in real estate), lingering Soviet-era illusionary longing (proven time and again, in the referendum for Lithuania's accession to the EU, and in the comparative EU citizens survey of 2006 evaluating the chosen EU socio-economic course); 2) obvious speculative attitudes in expectation of the introduction of the Euro; 3) a comparatively greater emigration trend, seen more in Lithuania when compared to other post-soviet countries.
Data sources
Average income--Department of Statistics
Loan interest rates--Bank of Lithuania
GDP--Department of Statistics
Average housing costs--State Enterprise Centre of Registers
Received 9 January 2008; accepted 17 June 2008
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Feliksas IVANAUSKAS (1), Rimantas EIDUKEVICIUS (2), Albinas MARCINSKAS (3) and Birute GALINIENE (4)([mail])
(1) Department of Computer Science, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko g. 24, LT-03225 Vilnius, Lithuania E-mail: feliksas.ivanauskas@maf.vu.lt
(2) Department of Mathematical Statistics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko g. 24, LT-03225 Vilnius, Lithuania E-mail: rimantas.eidukevicius@mif.vu.lt
(3) Department of Management, Faculty of Economics, Vilnius University, Sauletekio al. 9, LT-10222 Vilnius, Lithuania E-mail: albinas.marcinskas@ef.vu.lt
(4) Department of Economic Policy, Faculty of Economics, Vilnius University, Sauletekio al. 9, LT-10222 Vilnius, Lithuania E-mail: birute.galiniene@ef.vu.lt
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